Dirk Vermeir: bibliography

Open Answer Set Programming with Guarded Programs

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
ACM Transactions on Computational Logic (TOCL), 9(4): 1-53, 2008

tocl2008.pdf

Compiling fuzzy answer set programs to fuzzy propositional theories.

By Jeroen Janssen, Stijn Heymans, Martine De Cock and D. Vermeir.
Proceedings of ICLP2008 (24th International Conference on Logic Programming)Lecture Notes in Computer Science 5366, p. 362-376, Springer, 2008

iclp2008.pdf

Fuzzy Argumentation Frameworks.

By Jeroen Janssen, Martine De Cock and D. Vermeir.
Proceedings of IMPU 2008 (12th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems), pp.513-520, 2008

ipmu2008.pdf

Conditional Planning with External Functions.

By Davy Van Nieuwenborgh, Thomas Eiter and D. Vermeir.
Proceedings of the 9th International Conference on Logic Programming and Non Monotonic Reasoning (LPNMR 2007), pp.214-227, Springer LNCS 4483, 2007.

lpnmr2007.pdf

An Introduction to Fuzzy Answer Set Programming.

By Davy Van Nieuwenborgh, Martine De Cock and D. Vermeir.
Annals of Mathematics and Artificial Intelligence 50 (3-4), pp.363-388, Springer, 2007.

fasp_amai.pdf

Open answer set programming for the semantic web.

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Journal of Applied Logic 5(1), pp.144-169, Elsevier, 2007.

oasp_jal_05.pdf

Computing Fuzzy Answer Sets Using dlvhex.

By Davy Van Nieuwenborgh, Martine De Cock and D. Vermeir.
Proceedings of the 23rd International Conference on Logic Programming (ICLP 2007), Springer LNCS 4670, 2007.

fasp2hex.pdf

Hierarchical Decision Making in Multi-Agent Systems using Answer Set Programming.

By Davy Van Nieuwenborgh, Stijn Heymans, Marina De Vos and D. Vermeir.
Revised Selected and Invited Papers of the 7th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA-VII), Springer LNAI 4371, pp. 20-40, 2007.

climaproc2006.pdf

Conceptual Logic Programs.

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Annals of Mathematics and Artificial Intelligence (Special Issue on Answer Set Programming) 47 (1-2), pp.103-137, Springer, 2006.

amai2006.pdf

Fuzzy Answer Set Programming.

By Davy Van Nieuwenborgh, Martine De Cock and D. Vermeir.
Proceedings of the 10th European Conference on Logics in Artificial Intelligence (JELIA 2006), Springer LNAI 4160, pp. 359-372, 2006.

fasp.pdf

Approximating Extended Answer Sets.

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), IOS Press, pp. 462-466, 2006.

ecai2006.pdf

Cooperating Answer Set Programming.

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of the 22th International Conference on Logic Programming (ICLP 2006), Springer LNCS 4079, pp. 226-241, 2006.

casp.pdf

Reasoning with the Description Logic DLRO-≤ using Bound Guarded Programs.

By Stijn Heymans, Davy Van Nieuwenborgh, Dieter Fensel and D. Vermeir.
Proceedings of Reasoning on the Web workshop (RoW 2006), 2006.

row2006.pdf

Hierarchical Decision Making in Multi-Agent Systems using Answer Set Programming.

By Davy Van Nieuwenborgh, Stijn Heymans, Marina De Vos and D. Vermeir.
Proceedings of the 7th Workshop on Computational Logic in Multi-Agent Systems (CLIMA-VII), pp. 17-32, 2006.

clima2006.pdf

Guarded Open Answer Set Programming with Generalized Literals

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 4th International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2006), pp. 179-200, Springer LNCS 3861, 2006

foiks2006.pdf

Preferred Answer Sets for Ordered Logic Programs.

By Davy Van Nieuwenborgh and D. Vermeir.
Theory and Practice of Logic Programming, Vol. 6, No. 1&2, pp. 107-167, 2006.

Abstract

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a best answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjunction and some other formalisms such as logic programs with ordered disjunction. The approach is shown to be useful in several application areas, e.g. repairing database, where minimal repairs correspond to preferred answer sets.

tplp06.pdf

Guarded Open Answer Set Programming

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 8th International Conference on Logic Programming and Non Monotonic Reasoning (LPNMR 2005), pp. 92-104, Springer LNAI 3662, 2005.

Abstract

Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program's constants. We define a fixed point logic (FPL) extension of Clark's completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling a characterization of an answer set semantics by µLGF formulas. Finally, we relate guarded OASP to Datalog L I T E , thus linking an answer set semantics to a semantics based on fixed pointmodels of extended stratified Datalog programs. From this correspondence, we deduce 2-E X P T I M E -completeness of satisfiability checking w.r.t. (loosely) guarded programs.

lpnmr2005.pdf

Synthesis from Temporal Specifications Using Preferred Answer Set Programming

By Stijn Heymans, Davy Van Nieuwenborgh and Dirk Vermeir.
Proceedings of the ICTCS conference, Springer LNCS 3701, 2005

ictcs2005.pdf

Intelligence Analysis using Quantitative Preferences

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of Answer Set Programming: Advances in Theory and Implementation (ASP 2005), pp. 233-247, Research Press International, 2005.

Extending Conceptual Logic Programs with Arbitrary Rules

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of Answer Set Programming: Advances in Theory and Implementation (ASP 2005), pp. 27-41, Research Press International, 2005.

Nonmonotonic Ontological and Rule-Based Reasoning with Extended Conceptual Logic Programs

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 2nd European Semantic Web Conference (ESWC 2005), pp. 392-407, Springer LNCS 3532, 2005

Abstract

We present extended conceptual logic programs (ECLPs), for which reasoning is decidable and, moreover, can be reduced to finite answer set programming. ECLPs are useful to reason with both ontological and rule-based knowledge, which is illustrated by simulating reasoning in an expressive description logic (DL) equipped with DL-safe rules. Furthermore, ECLPs are more expressive in the sense that they enable nonmonotonic reasoning, a desirable feature in locally closed subareas of the Semantic Web.

eswc2005.pdf

Weighted Answer Sets and Applications in Intelligence Analysis

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, pp. 169-183, Springer LNAI 3452, 2005.

Abstract

The extended answer set semantics for simple logic programs, i.e. programs with only classical negation, allows for the defeat of rules to resolve contradictions. In addition, a partial order relation on the program's rules can be used to deduce a preference relation on its extended answer sets. In this paper, we propose a "quantitative" preference relation that associates a weight with each rule in a program. Intuitively, these weights define the "cost" of defeating a rule. An extended answer set is preferred if it minimizes the sum of the weights of its defeated rules. We characterize the expressiveness of the resulting semantics and show that it can capture negation as failure. Moreover the semantics can be conveniently extended to sequences of weight preferences, without increasing the expressiveness. We illustrate an application of the approach by showing how it can elegantly express subgraph isomorphic approximation problems, a concept often used in intelligence analysis to find specific regions of interest in a large graph of observed activities.

lpar2004.ps.gz, lpar2004.pdf

An Ordered Logic Program Solver

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of the 7th International Symposium on Practical Aspects of Declarative Languages (PADL 2005), pp. 128-142, Springer LNCS 3350, 2005.

Abstract

We describe the design of the OLPS system, an implementation of the preferred answer set semantics for ordered logic programs. The basic algorithm we propose computes the extended answer sets of a simple program using an intuitive 9-valued lattice, called T9. During the computation, this lattice is employed to keep track of the status of the literals and the rules while evolving to a solution. It turns out that the basic algorithm needs little modification in order to be able to compute the preferred answer sets of an ordered logic program. We illustrate the system using an example from diagnostic reasoning and we present some preliminary benchmark results comparing OLPS with existing answer set solvers such as SMODELS and DLV.

padl2005.pdf

On Programs with Linearly Ordered Multiple Preferences

By Davy Van Nieuwenborgh, Stijn Heymans and D. Vermeir.
Proceedings of the 20th International Conference on Logic Programming (ICLP 2004), pp. 180-194, Springer LNCS 3132, 2004.

Abstract

The extended answer set semantics for logic programs allows for the defeat of rules to resolve contradictions. We propose a refinement of these semantics based on a preference relation on extended literals. This relation, a strict partial order, induces a partial order on extended answer sets. The preferred answer sets, i.e. those that are minimal w.r.t. the induced order, represent the solutions that best comply with the stated preference on extended literals. In a further extension, we propose linearly ordered programs that are equipped with a linear hierarchy of preference relations. The resulting formalism is rather expressive and essentially covers the polynomial hierarchy. E.g. the membership problem for a program with a hierarchy of height n is at the n+1 level of the polynomial hierarchy. We illustrate an application of the approach by showing how it can easily express hierarchically structured weak constraints, i.e. a layering of ``desirable'' constraints, such that one tries to minimize the set of violated constraints on lower levels, regardless of the violation of constraints on higher levels.

iclp2004.ps.gz, iclp2004.pdf

Hierarchical Decision Making by Autonomous Agents

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 9th European Conference on Logics in Artificial Intelligence (JELIA 2004), pp. 44-56, Springer LNCS 3229, 2004.

Abstract

Often, decision making involves autonomous agents that are structured in a complex hierarchy, representing e.g. authority. Typically the agents share the same body of knowledge, but each may have its own, possibly conflicting, preferences on the available information. We model the common knowledge base for such preference agents as a logic program under the extended answer set semantics, thus allowing for the defeat of rules to resolve conflicts. An agent can express its preferences on certain aspects of this information using a partial order relation on either literals or rules. Placing such agents in a hierarchy according to their position in the decision making process results in a system where agents cooperate to find solutions that are jointly preferred. We show that a hierarchy of agents with either preferences on rules or on literals can be transformed into an equivalent system with just one type of preferences. Regarding the expressiveness, the formalism essentially covers the polynomial hierarchy. E.g. the membership problem for a hierarchy of depth n is at the n+2 level of the polynomial hierarchy. We illustrate an application of the approach by showing how it can easily express a generalization of weak constraints, i.e. ``desirable" constraints that do not need to be satisfied but where one tries to minimize their violation.

jelia2004.ps.gz, jelia2004.pdf

Semantic Web Reasoning with Conceptual Logic Programs

By Stijn Heymans, Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 3th International Workshop on Rules and Rule Markup Languages for the Semantic Web (RuleML 2004), pp. 113-127, Springer LNCS 3323, 2004.

Abstract

We extend Answer Set Programming with, possibly infinite, open domains. Since this leads, in general, to undecidable reasoning, we restrict the syntax of programs, while carefully guarding useful knowledge representation mechanisms such as negation as failure and inequalities. Reasoning with the resulting Conceptual Logic Programs can be reduced to finite, normal Answer Set Programming, for which reasoners are available. We argue that Conceptual Logic Programming is a useful tool for uniformly representing and reasoning with both ontologies and rules on the Semantic Web, as they can capture a large fragment of the OWL DL ontology language, while extending it in various aspects.

ruleml2004.ps.gz, ruleml2004.pdf

Extending Answer Sets for Logic Programming Agents

By Marina De Vos and D. Vermeir.
Annals of Mathematics and Artificial Intelligence, Vol. 42, No 1-3, pp. 103--139, 2004.

Integrating Description Logics and Answer Set Programming.

By Stijn Heymans and D. Vermeir.
Principles and Practice of Semantic Web Reasoning (PPSWR03), pp. 146-159, Springer LNCS 2901, 2003.

ppswr2003.ps.gz, ppswr2003.pdf

Order and Negation as Failure

By Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 19th International Conference on Logic Programming (ICLP2003), pp. 194-208, Springer LNCS 2916, 2003.

Abstract

We equip ordered logic programs with negation as failure, using a simple generalization of the preferred answer set semantics for ordered programs. This extension supports a convenient formulation of certain problems, which is illustrated by means of an intuitive simulation of logic programming with ordered disjunction. The simulation also supports a broader application of ``ordered disjunction'', handling problems that would be cumbersome to express using ordered disjunction logic programs. Interestingly, allowing negation as failure in ordered logic programs does not yield any extra computational power: the combination of negation as failure and order can be simulated using order (and true negation) alone.

iclp2003.ps.gz, iclp2003.pdf

Integrating Semantic Web Reasoning and Answer Set Programming.

By Stijn Heymans and D. Vermeir.
Answer Set Programming: Advances in Theory and Implementation (ASP03), pp. 194-208, CEUR Proceedings Vol. 78.

asp2003.ps.gz, asp2003.pdf

Ordered Diagnosis.

By Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 10th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR2003), pp. 244-258, Springer LNAI 2850, 2003.

Abstract

We propose to regard a diagnostic system as an ordered logic theory, i.e. a partially ordered set of clauses where smaller rules carry more preference. This view leads to a hierarchy of the form observations < system description <fault model, between the various knowledge sources. It turns out that the semantics for ordered logic programming nicely fits this intuition: if the observations contradict the normal system behavior, then the semantics will provide an explanation from the fault rules. The above model can be refined, without adding additional machinery, to support e.g. problems where there is a clear preference among possible explanations or where the system model itself has a complex structure. Interestingly, these extensions do not increase the complexity of the relevance or necessity decision problems. Finally, the mapping to ordered logic programs also provides a convenient implementation vehicle.

lpar2003.ps.gz, lpar2003.pdf

Integrating Ontology Languages and Answer Set Programming.

By Stijn Heymans and D. Vermeir.
Proceedings of the 14th International Workshop on Expert System Applications (DEXA2003), pp. 584-588, IEEE Computer Society, 2003.

Abstract

We integrate ontology languages and logic programming (LP) by extending disjunctive logic programs (DLPs) and their semantics in order to support inverses and an infinite universe, without introducing function symbols. We show that this extension is still decidable, and can be used to simulate, on the one hand, answer set programming with a finite universe, and on the other hand, several expressive description logics (DLs), which can be seen as ontology languages. The integration leads to a ``best of both worlds": from the LP side it inherits a flexible and intuitive representation of knowledge, whereas the DLs side provides the possibility to represent infinite knowledge.

dexa2003.ps.gz, dexa2003.pdf

Ordered Programs as Abductive Systems

By Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the APPIA-GULP-PRODE Conference on Declarative Programmaing, pp. 274-385, 2003.

Abstract

In ordered logic programs, i.e. partially ordered sets of clauses where smaller rules carry more preference, inconsistencies, which appear as conflicts between applicable rules, are handled by satisfying more preferred rules, at the expense of defeating lesser rules.

We show that this formalism can be exploited to obtain a simple implementation of abductive systems, where abducibles are assumed false by default, but weaker rules can be used to introduce them, if necessary. Moreover, the approach can be extended, without leaving the ordered programming framework, to support abductive systems involving preference, either on the set of abducibles or on the system description. The latter case appears naturally in applications such as legal reasoning where rules carry a natural precedence.

However, combining preference on abducibles with a complex theory structure brings the complexity, e.g. of the relevance problem, to Σ3, and thus such systems cannot be simulated by ordered programs.

agp2003.ps.gz, agp2003.pdf

Dynamic Decision Making in Logic Programming and Game Theory

By Marina De Vos and D. Vermeir.
AI2002: Advances in Artificial Intelligence, Springer Verlag, Lecture Notes in Artificial Intelligence. pp. 36-57, 2002.

ai2002.ps.gz, ai2002.pdf

Logic Programming Agents Playing Games

By Marina De Vos and D. Vermeir.
In Research and Development in Intelligent Systems XIX (ES2002) Springer Verlag, BCS Conference Series, pp. 323-336, 2002.

es2002.ps.gz, es2002.pdf

A Defeasible Ontology Language.

By Stijn Heymans and D. Vermeir.
Proceedings of the 2002 ODBASE International Conference , Springer Verlag, Lecture Notes in Computer Science 2519, pp. 1033-1046, 2002.

odbase2002.ps.gz, odbase2002.pdf

Preferred Answer Sets for Ordered Logic Programs.

By Davy Van Nieuwenborgh and D. Vermeir.
Proceedings of the 8th European Conference on Logics in Artificial Intelligence (JELIA2002), pp. 432-443, Springer LNAI 2424, 2002.

Abstract

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure as well as disjunction. We illustrate an application of the approach by considering database repairs, where minimal repairs are shown to correspond to preferred answer sets.

jelia2002.ps.gz jelia2002.pdf

Using Preference Order in Ontologies.

By Stijn Heymans and D. Vermeir.
Proceedings of the 13th International Workshop on Expert System Applications (DEXA2002), pp. 85-89, IEEE Computer Society, 2002.

Abstract

The latest ontology languages can be translated into a description logic (DL), thus providing them with a formal semantics and associated reasoning procedures. We introduce the ordered description logic OSHOQ(D) as a simple decidable extension of SHOQ(D) that supports the direct definition of a preference order on defeasible axioms, thus allowing for a succinct and intuitive expression of defeasible ontologies, containing e.g. exceptions for certain axioms. We demonstrate the usefulness of OSHOQ(D) for solving inconsistencies that may appear e.g. when merging existing ontologies. We present an algorithm that, based on concrete examples of facts that should be true, produces minimal preference orderings on the axioms, in order to make an otherwise inconsistent knowledge base consistent.

dexa2002.ps.gz, dexa2002.pdf

Semantic Forcing in Disjunctive Logic Programs.

By Marina De Vos and D. Vermeir.
Computational Intelligence, Vol. 17, No. 4, pp. 651-684, 2001.

Abstract

We propose a semantics for disjunctive logic programs, based on the single notion of forcing. We show that the semantics properly extends, in a natural way, previous approaches. A fixpoint characterization is also provided. We also take a closer look at the relationship between disjunctive logic programs and disjunctive-free logic programs. We present certain criteria under which a disjunctive program is semantically equivalent with its disjunctive-free (shifted) version.

forcing.ps.gz, forcing.pdf

Decisions, Agents and Game Theory.

By Marina De Vos and D. Vermeir.
In Theoretical aspects of Rationality and Knowledge (TARK 2001), pp. 219--232. Morgan Kaufmann, 2001.

tark2001.ps.gz, tark2001.pdf

Multi-Paradigm Programming using C++

By D. Vermeir.
Springer-Verlag London, 2001, 287pp. ISBN 1-85233-483-5.

Logic Programming Agents and Game Theory.

By Marina De Vos and D. Vermeir.
In Answer Set Programming: Towards Efficient and Scalable Knowledge Representation and Reasoning, pp. 27--33. American Association for Artificial Intelligence Press, Stanford (Palo Alto), California, US, 2001.

Abstract

In this paper we present a framework for logic programming agents to take part in games in such a way that stable models of the system, the ones agreed upon by all the members, correspond with the different equilibria of the game. The proposed transformations from games to ordered choice logic program produces a multi-agent system where each agent embodies the reasoning of a player and where the system itself represents the structure of the game. This allows us to monitor the knowledge and beliefs of the agents, i.e. the flow of information between agents/players.

asets.ps.gz, asets.pdf

Dynamically Ordered Probabilistic Choice Logic Programming

By Marina De Vos and D. Vermeir
Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS2000), pp. 227 - 239, Springer LNCS 1974, 2000.

Abstract

We present a framework for decision making under uncertainty where the priorities of the alternatives can depend on the situation at hand. We design a logic-programming language, DOP-CLP, that allows the user to specify the static priority of each rule and to declare, dynamically, all the alternatives for the decisions that have to be made. In this paper we focus on a semantics that reflects all possible situations in which the decision maker takes the most rational, possibly probabilistic, decisions given the circumstances. Our model theory, which is a generalization of classical logic-programming model theory, captures uncertainty at the level of total Herbrand interpretations. We also demonstrate that DOP-CLPs can be used to formulate game theoretic concepts.

fsttcs2000.ps.gz, fsttcs2000.pdf

A Logic for Modeling Decision Making with Dynamic Preferences

By Marina De Vos and D. Vermeir
Proceedings of the Logics in Artificial Inteligence (jelia2000) workshop, pp. 391-406, Springer LNAI 1919, 2000.

Abstract

We present a framework for decision making with the possibility to express circumstance-dependent preferences among different alternatives for a decision. This new formalism, Ordered Choice Logic Programs (OCLP), builds upon choice logic programs to define a preference/specialization relation on sets of choice rules. We show that our paradigm is an intuitive extension of both ordered logic and choice logic programming such that decisions can comprise more than two alternatives which become only available when a choice is actually forced. The semantics for OCL programs is based on stable models for which we supply a characterization in terms of assumption sets and a fixpoint algorithm. Furthermore we demonstrate that OCLPs allow an elegant translation of finite extensive games with perfect information such that the stable models of the program correspond, depending on the transformation, to either the Nash equilibria or the subgame perfect equilibria of the game.

jelia2000.ps.gz, jelia2000.pdf

A Universal Fixpoint Semantics for Ordered Logic

By Els Laenens and D. Vermeir
Computers and Artificial Intelligence, Vol. 19, No 3, 2000.

On the role of negation in choice logic programs

By Marina De Vos and D. Vermeir
Proceedings of the 5th international conference on logic programming and nonmonotonic reasoning (lpnmr99), pp. 236-246, Springer LNCS 1730, 1999.

Abstract

We introduce choice logic programs as negation-free datalog programs that allow rules to have exclusive-only (possibly empty) disjunctions in the head. Such programs naturally model decision problems where, depending on a context, agents must make a decision, i.e. an exclusive choice out of several alternatives. It is shown that such a choice mechanism is in a sense equivalent with negation as supported in semi-negative (``normal'') datalog programs. We also discuss an application where strategic games can be naturally formulated as choice programs: it turns out that the stable models of such programs capture exactly the set of Nash equilibria. We then consider the effect of choice on ``negative information'' that may be implicitly derived from a program. Based on an intuitive notion of unfounded set for choice programs, we show that several results from (seminegative) disjunctive programs can be strengthened; characterizing the position of choice programs as an intermediate between simple positive programs and programs that allow for the explicit use of negation in the body of a rule.

lpnmr99.ps.gz, lpnmr99.pdf

Choice Logic Programs and Nash Equilibria in Strategic Games

By Marina De Vos and D. Vermeir
Proceedings of the 13th CSL'99 conference, pp.266-276, Springer LNCS 1683, 1999.

Abstract

We define choice logic programs as negation-free datalog programs that allow rules to have exclusive-only disjunctions in the head. We show that choice programs are equivalent to semi-negative datalog programs, at least as far as stable models are concerned. We also discuss an application where strategic games can be naturally formulated as choice programs; it turns out that the stable models of such programs capture exactly the set of Nash equilibria.

csl99.ps.gz, csl99.pdf

Dialectic semantics for argumentation frameworks

By H. Jakobovits and D. Vermeir
Proceedings of the seventh international conference on artificial intelligence and law, pp. 63-62, ACM publications, 1999.

Abstract

We provide a formalism for the study of dialogues, where a dialogue is a two-person game, initiated by the proponent who defends a proposed thesis.

We examine several different winning criteria and several different dialogue types, where a dialogue type is determined by a set of positions, an attack relation between positions and a legal-move function. We examine two proof theories, where a proof theory is determined by a dialogue type and a winning criterion. For each of the proof theories we supply a corresponding declarative semantics.

icail99.ps.gz, icail99.pdf

Robust Semantics for Argumentation Frameworks

By H. Jakobovits and D. Vermeir
Journal of Logic and Computation, Vol. 9, No. 2, pp. 215-261, 1999.

Abstract

We suggest a so-called ``robust'' semantics for a model of argumentation which represents arguments and their interactions, called ``argumentation frameworks''. We study a variety of additional definitions of acceptability of arguments; we explore the properties of these definitions; we describe their inter-relationships: e.g. robust models can be characterized using the minimal (well-founded) models of a meta-framework. The various definitions of acceptability of argument sets can all deal with contradiction within an argumentation framework.

arguments.ps.gz, arguments.pdf

Defeasible Logics

By P. Geerts and D. Vermeir.
In ``Handbook of defeasible reasoning and uncertainty management systems, Vol. 2: Reasoning with Actual and Potential Contradictions'', eds. D. M. Gabbay and P. Smets, pp.175-210, Kluwer Academic Press, 1998.

Abstract

We present an overview of the defeasible approach to nonmonotonic reasoning, as opposed to the minimalist approach and the fixpoint approach. Formalisms following the minimalist approach, like circumscription, look at models of a classical theory that are minimal with respect to some set of predicates occurring in the theory. Fixpoint formalisms include McDermott's and Doyle's nonmonotonic logic, Reiter's default logic, and Moore's autoepistemic logic.
Default rules in these systems involve a special condition for application, which is explained in the proof theory. By applying rules in an arbitrary order, some other rules may become blocked, and eventually, a fixpoint is derived from where no new conclusions can be reached. At a fixpoint, every default is either inapplicable or applied. The same holds for minimal models.
In the defeasible approach, defaults are treated quite differently. The intent of a default A -> p is that p will normally be derivable from a theory containing this default whenever A is derivable. However, it is possible to have a theory containing A -> p from which both A and not(p) can be derived. If this is the case, the rule A -> p is said to be defeated.
Rules which can be defeated are called defeasible rules and logics using defeasible rules are called defeasible logics. In a defeasible logic formalism, extensions of theories are formed, in which each rule is either inapplicable, applied or defeated.

drums_book.ps.gz, drums_book.pdf

Contradiction in Argumentation Frameworks

By H. Jakobovits and D. Vermeir.
Proceedings of the 1996 conference on Information Processing and Management of Uncertainty (IPMU96), pp 821-826, 1996.

Abstract

We present a theory of argumentation that can deal with contradiction within an argumentation framework, thus solving a problem posed in [Dung95].

By representing logic programs as sets of interacting arguments, we can apply our results for general argumentation frameworks to logic-programming semantics. This yields a new semantics for logic programs that properly extends traditional approaches such as stable and well-founded models.

ipmu96.ps.gz, ipmu96.pdf

r-stable models for logic programs

By H. Jakobovits and D. Vermeir.
Springer Verlag, Lecture Notes in Computer Science 1154, pp 233-244, 1996.

Abstract

We propose a new semantics for general logic programs which stems from first principles of logic-programming semantics. Our theory unifies previous approaches and is applicable to some useful programs which are not properly handled by existing semantics.

lid96.ps.gz, lid96.pdf

Dirk Vermeir (dvermeir@vub.ac.be) [Last modified: Sat Nov 12 10:53:45 MET 2005 ]